I have a doubt , please help me out !!

In the given figure , P , Q , R are 3 complex numbers . Angle PQR = \(\theta\)

How do I represent theta using only the amplitudes of the given complex numbers ?

Also if \(Z_1 Z_2 Z_3\) be 3 complex numbers taken in the complex plane in the anticlockwise sense , then how can I represent the angle \(Z_1 Z_2 Z_3\) in terms of the individual amplitudes of the complex numbers ?

P.S. The angles/amplitude part of the complex numbers is the only thing that has kept me confused , the other parts ar clear to me . Please help me out !!

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## Comments

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TopNewestI'm assuming that by amplitudes you mean magnitudes. I don't know if there is an equation exclusively in terms of the magnitudes, but this link discusses the dot product adapted for complex vectors, from which you can determine \(\theta.\)

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Thanks for the link sir . But I was referring to the angle made by the complex number with the origin sir as in argument of a complex number .

I am not able to understand the concept of arg \(\frac{Z_1 - Z_2}{Z_3-Z_2}\) , what does it mean and how to use it in calculations ? This is my doubt sir , please see the pic that I have provided sir ?

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